User talk:R.e.b.

Commutative von Neumann regular rings

Howdy, I changed the "Commutative vN regular if and only if subring of fields" to "only if", but I think more is true. It is not completely iff, since an integral domain that is not a field is never vN regular (Frac(D)/D is not flat). However, the point really is that these rings are special subrings of infinite direct products of fields that act very much like direct products of fields. I couldn't find a reference, but I think it was something like "subrings such that the projection map for each factor is surjective". So "1 + Sum(K_i)" as a subring of "Prod(K_i)" should be vN regular, and should be something similar to the "ring of compact operators with 1 adjoined".

I tend to stick with finite or at least very special rings these days, so I could easily be wrong. I figured if you had the reference at hand, it would be easy to fix. Otherwise I'll check Goodearl's text sometime this week. JackSchmidt (talk) 18:09, 27 February 2008 (UTC)

I'm at least a little wrong. Every von Neumann regular ring is semiprimitive, and the commuative semiprimitive rings are the ones I described (subdirect products of fields). So there are some subdirect products of fields that are not von Neumann regular. Hopefully the "reduced and Krull dimension 0" characterisation is useful enough. Please let me know if you find a nice if and only if along the lines of subrings of fields. JackSchmidt (talk) 18:34, 27 February 2008 (UTC)

You are right; I was not paying attention when I wrote that, and meant to say "subring of a product of fields that is closed under taking quasi-inverses". R.e.b. (talk) 19:43, 27 February 2008 (UTC)

Thanks for fixing this, and for the steady stream of improvements to the math articles. I enjoy checking my watchlist, and reading your new additions every few days. It is like an eclectic course on all things interesting. You've even convinced me model theory is worth my time to learn, though it might be a few years before I need more than wikipedia already has on the subject. Thanks again, JackSchmidt (talk) 05:51, 3 March 2008 (UTC)

Model companion

A tag has been placed on Model companion, requesting that it be speedily deleted from Wikipedia. This has been done under the criteria for speedy deletion, because it is a redirect to a nonexistent page.

If you can fix this redirect to point to an existing Wikipedia page, please do so and remove the speedy deletion tag. However, please do not remove the speedy deletion tag unless you also fix the redirect. Feel free to leave a note on my talk page if you have any questions about this. -WarthogDemon 19:07, 29 February 2008 (UTC)

{{citation}}

I was fulfilling an editprotected request, where the author had made a one-character error that nonetheless made a huge mess. I hope I've now fixed the problem - let me know if there are any outstanding errors and I'll revert and let them work out what's wrong. Happy‑melon 15:56, 3 March 2008 (UTC)

For the caching issue, see WP:BYC#Server cache: it's slightly quicker to purge than make a trivial edit. Geometry guy 17:10, 3 March 2008 (UTC)

Sync of the ordinal analysis and large countable ordinal articles

Hi! I agree with the move of creating the article on ordinal analysis, however I draw your attention to the existence of the article on large countable ordinals: it would be nice to keep them from overlapping too much, by moving material from one to the other, and by adding abundant links. I did a bit of that, I'll let you judge of what else needs to be done. (Unfortunately we have quite a mess of ordinal-related articles sharing much of the same content without clear relations between them.) --Gro-Tsen (talk) 19:06, 4 March 2008 (UTC)

Thanks. I already know about large countable ordinals (having written some of it in the days before it was split off). I was wondering whether to give Feferman-Schutte and Bachmann-Howard ordinals their own articles, but havn't yet decided whether this would make the ordinal mess better or worse. R.e.b. (talk) 19:35, 4 March 2008 (UTC)

Hoax?

Hello. Do you know anything about Troy Raeder? It has been suggested that the article is a hoax. Michael Hardy (talk) 15:59, 5 March 2008 (UTC)

Yes, its a hoax. R.e.b. (talk) 16:01, 5 March 2008 (UTC)

...and I now see that the person who created it has no other edits. Michael Hardy (talk) 16:14, 5 March 2008 (UTC)

Iwasawa decomposition and unipotent

Howdy, I wanted to salvage NBarth's edit, but I don't know enough math to handle part of it. I think it might be nice to phrase the example also in a "basis-free way", so that one could link to unipotent. Basically, the factorization is KAN, where K is a ???, A is a "maximal torus", and N is a "maximal unipotent subgroup" or "the unipotent radical of the normalizer of A" or something. K seems a little like a Weyl group, but I don't think it is (seems to contain it as a small subgroup). Is there something like this that is true? Maybe more specific questions are easier:

• Is A a maximal torus?
• Does A always normalize N?
• Is N always the unipotent radical of the normalizer of A?
• Is K a "Cartan subgroup"?

Thanks for any help, and no worries if they don't sound sane to answer. I'm still trying to learn this material, so there is no reason at all to think my questions are on target. JackSchmidt (talk) 00:54, 9 March 2008 (UTC)

• A is not a maximal torus, but is a connected component of a maximal split torus (where "torus" is used in the algebraic group sense, not the Lie group sense).
• Yes, A normalizes N
• N is almost never the unipotent radical of the normalizer of A.
• K is a maximal compact subgroup, and has little to do with Cartan subgroups.

These apply if G is well behaved (connected, semisimple, etc); I'd have to think more carefully about the general case. R.e.b. (talk) 01:10, 9 March 2008 (UTC)

Re Request for expert help

Request for expert help

The new article Landau-Lifshitz equation needs some expert help in expanding it; your comments suggest you might know about this topic.

As you have probably figured out by now, it is a complete waste of your time to argue with rude and ignorant editors about topics they do not understand. Wikipedia has an unlimited supply of such editors, and it is best just to ignore them. R.e.b. (talk) 19:28, 25 March 2008 (UTC)

• Thanks for the offer, and the consoling remarks, but I am afraid I will not have the time to help on this. In fact - although it is obviously with good intentions, the equation that you have identified as the Landau-Lifschitz equation is not the right one. There are more than one equations going under this name. The ones being referred to in the discussion in hand are PDE's with one time and either one, or two space variables. This one is an ODE, with only time, an external magnetic field, and no space variables. (i.e. the PDE's represent a field theory of magnetism; these ODE's just represent the motion of a single spinning, charged object in an external magnetic field. A different problem.)

If you would like a good source for the correct L.L. equations, try looking up the book: L.D. Faddeev, L. A. Takhtajan (1987). Hamiltonian Methods in the Theory of Solitons. Addison-Wesley. ISBN 0387155791, ISBN 978-0387155791. R_Physicist (talk) 19:58, 25 March 2008 (UTC)